a) Figure 3 illustrates the general architecture of a service in a public-key cryptosystem. Assume that Abdullah needs to send a secret message to Aminah. Study the figure and answer the following questions. (Tips: E Encrypt, D Decrypt)

i) State the service(s) that can be provided by the architecture. (1 mark)

ii) If Abdullah needs to sign the message, write the full function of the ciphertext to be sent. (2 marks)

iii) Write the function of decryption. (2 marks)

b) Consider the RSA cryptosystem is used to encrypt a message M = 14. Given p = 3, q = 5, and e = 7, calculate the value of the private key. Show all your workings step by step involved clearly. (7 marks)

c) Consider the RSA cryptosystem is used to encrypt a message, M. Given the p = 3, q = 11, e = 7, and d = 3 . If the public key is used to generate the ciphertext, C = 16, calculate the value of M. Show your workings. (4 marks)

d) Consider the RSA cryptosystem is used by Ahmad to authenticate a message, M = 7. Given the Ahmads private key = {3, 22} and the Ahmads public key = {7, 22}. Proof the ciphertext, C = 13 received by Azizah either is original or not original from the sender and justify your answer. Show your workings. (4 marks)

W X W Message Encryption algorithm Decryption algorithm Message : , Key pair source Key2 Key pair source Figure 3: Public-key cryptosystem W X W Message Encryption algorithm Decryption algorithm Message : , Key pair source Key2 Key pair source Figure 3: Public-key cryptosystem